# Computational Framework for L$$_{2}$$E Structured Regression Problems

The L2E package (version 2.0) implements the computational framework for L$$_2$$E regression in Liu, Chi, and Lange (2022+), which was built on the previous work in Chi and Chi (2022). Both works employ the block coordinate descent strategy to solve a nonconvex optimization problem but utilize different methods for the inner block descent updates. We refer to the method in Liu, Chi, and Lange (2022+) as “MM” and the one in Chi and Chi (2022) as “PG” in our package. This package provides code to replicate some examples illustrating the usage of the frameworks in both manuscripts.

## Installation

To install the latest stable version from CRAN:

install.packages('L2E')

To install the latest development version from GitHub:

# install.packages("devtools")
devtools::install_github('jocelynchi/L2E-package-demo')

## Getting Started

We’ve included an introductory demo on how to use the L2E framework with examples from the accompanying journal manuscripts.

## Citing the package

Please reference the following manuscripts when citing this package. Thank you!


@article{L2E-Chi,
title={A User-Friendly Computational Framework for Robust Structured Regression with the L$_2$ Criterion},
author={Chi, Jocelyn T. and Chi, Eric C.},
journal={Journal of Computational and Graphical Statistics},
pages={1--12},
year={2022},
publisher={Taylor \& Francis}
}

@article{L2E-Liu,
title={A Sharper Computational Tool for L$_2$E  Regression},
author={Liu, Xiaoqian and Chi, Eric C. and Lange, Kenneth},
journal={arXiv preprint arXiv:2203.02993},
year={2022}
}